1. Field of the Invention
The present invention relates generally to imaging methods and systems, and more particularly to methods and systems for reducing distortion of single-viewpoint projections derived from images captured by non-single viewpoint imaging systems.
2. Description of the Related Art
A typical imaging system receives one or more rays of light from each point in a scene being imaged. In a classic “pinhole” camera, a single ray of light is received from each scene point and is projected upon one point of a detector (e.g., a piece of film or CCD image detector array). In an imager which uses one or more lenses to collect more light than would otherwise be collected using a simple pinhole camera, a bundle of light rays is received from each scene point and is focused onto a single point of a focal plane within the imager. Each bundle of light emanating from a scene point is considered to have a chief ray which can be used to define the direction in which the scene point is located with respect to the field of view of the imager. Many conventional imaging systems are designed to have a single “viewpoint”—a point of intersection of all of the chief rays of the bundles of light received from the various scene points. The viewpoint can also be referred to as a “virtual pinhole”.
FIG. 5A schematically illustrates an example of a single viewpoint imaging system. Incoming light rays 504 are effectively received by the system through a single viewpoint 502. The incoming light rays are projected—either directly or through internal optical components—onto an imaging plane 510 in the form of rays 508. A detector 506—which can include, for example, a piece of film or a CCD image detector array—is located at the imaging plane 510, and receives and detects the internal rays 508. The detector 506 generates, from the internal rays 508, an image which is a “perspective projection” of the scene as it would look if viewed directly from the virtual viewpoint 502.
The concept of a perspective projection can be further understood with reference to FIG. 5B. From a virtual viewpoint 502, geometric rays 514 and 524 can be considered to extend to various points (e.g., point 522) in the scene 512. If an arbitrarily-defined projection plane 510 is located between the virtual viewpoint 502 and the scene 512, a ray 514 extending from the viewpoint 502 to a scene point 522 intersects the plane 510 at a point 516. The set of points 516 in the projection plane 510 can be pixels representing, e.g., the brightness of each of the scene points 522. The set of such points 516 is considered to be a perspective projection (a/k/a/ a “perspective view”). It is desirable to obtain a perspective view (i.e., a perspective projection) of the scene 512, because within the field of view covered by the perspective projection, any other arbitrary perspective projection can be generated—i.e., a perspective projection can be generated using any other arbitrary plane. Furthermore, any arbitrary perspective projection of the scene 512—if viewed from the same distance and direction as those of the viewpoint 502 from which the perspective projection was generated—looks exactly as the scene 512 would look if viewed directly.
FIG. 5B also illustrates the projection of the scene 512 onto a cylinder 520. Such a projection can be referred to as a “panoramic projection.” For example, a point 518 on the panoramic projection would be located at the intersection of ray 514 and the cylinder 520. Similarly, to a perspective projection, a panoramic projection can also be used to reconstruct how the scene would look if viewed directly from the viewpoint 502 used to generate the panoramic projection.
However, many imaging systems do not have a single viewpoint; in other words, not all of the chief rays of the bundles of light rays received by the imager intersect at a single point. Non-single viewpoint imagers can provide advantages such as wider field of view. However, unlike an image captured from a single viewpoint imager, an image captured by a non-single viewpoint imager typically cannot be used to generate an accurate, undistorted perspective view—or, in fact, any other single-viewpoint image—unless additional information regarding the scene geometry is available.
An example of a typical, non-single viewpoint imaging system is a fish-eye lens based system. Such a system is illustrated in FIG. 6. The illustrated system includes front objective lenses 606 which receive incoming rays 608. The incoming light is sent to a set of relay lenses 604 which focus the light unto an imaging plane 602. Such a system which includes lenses, but no reflective elements, can be referred to as a “dioptric” system.
Some imaging systems utilize reflective elements, rather than lenses, to capture images. Such systems can be referred to as “catoptric” systems. Examples of catoptric imaging systems are illustrated in FIGS. 7A, 7B, and 7C. Each of the systems 702 illustrated in FIGS. 7A, 7B, and 7C includes a pinhole camera 704 having a pinhole 708, and a reflector 706. In the system illustrated in FIG. 7A, the reflector 706 is spherical, and the camera 704 is positioned directly above the reflector 706. Such a system is an example of a catoptric system which does not have a single viewpoint. Accordingly, an image captured with such a system would not be a perspective view. The system can also be configured such that the camera 704 is not directly above the reflector 706, as illustrated in FIG. 7B. Furthermore, although the reflector 706 in the systems 702 illustrated in FIGS. 7A and 7B is spherical, non-spherical reflector surfaces have also been used, as illustrated in FIG. 7C.
In addition, although the above discussion refers to a camera 704 having an actual pinhole 708, most conventional cameras include lenses. Such a lens-based camera, if used as the camera 704 in one of the systems illustrated in FIGS. 7A, 7B, and 7C, would form a system including both mirrors and lenses. Such a system having both mirrors and lenses can be referred to as a “catadioptric” system.
Catadioptric systems such as those illustrated in FIGS. 7A, 7B, and 7C are capable of imaging extremely wide fields of view—significantly greater than 180° in certain configurations. However, such systems typically tend to be non-single viewpoint systems. Consequently, the wide field of view is obtained by sacrificing the ability to generate undistorted perspective views.